Quantum Cournot duopoly game with general isoelastic demand and asymmetric production costs

¹ School of Mathematics, Liaoning Normal University - Dalian 116029, China
² School of Economics and Management, China University of Petroleum - Qingdao 266580, China

^(a) 2491817437@qq.com (corresponding author)

Received: 16 January 2022
Accepted: 30 May 2022

Abstract

This letter explores the quantum version of a Cournot duopoly game with general isoelastic demand and asymmetric production costs by applying Li-Du-Massar's minimal quantization rules, and it especially analyzes the existence region of quantum equilibrium, and the influences of quantum entanglement , difference in marginal costs (k) and elasticity of demand on the optimal profits of both firms. The results show that the existence region decreases with γ and k increasing. A larger elasticity of demand can destroy the profits of both firms. If positive γ and k are more favourable to the profits of two firms. If the first firm's profit increases with γ increasing for fixed k, but decreases with k increasing for fixed γ. The second firm's profit increases with k increasing for any fixed γ. As to the influences of γ on the second firm's profit, when k is less than a critical value, it increases with γ increasing, otherwise it decreases with γ increasing for fixed k.